Generalizations of the Scorza correspondence

2026/07/24 by Maria Teresa Ruggiero
#math.AG

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Abstract

We study generalizations of the Scorza correspondence associated with a general (C,η) in the moduli space of even spin curves S_g⁺. We first give a new proof of the smoothness of the classical Scorza curve, originally established by Farkas-Verra. We then introduce higher order analogues of the Scorza correspondence and investigate their geometry. In particular, we compute their classes in the Néron-Severi group and study their singularities and genera. Finally, we consider a higher-dimensional version of the construction and focus on the threefold case, where we describe its class and prove a smoothness result outside a naturally defined degeneracy locus.

Citations

• Ulrich sheaves and determinantal representations for higher secant varieties of curves

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